Physics - Understanding the Relationship Between Force and Acceleration

A car rounds a perfectly circular turn at a constant speed. This causes the acceleration to __________.

remain constant

increase

decrease

become zero

not be predictable

Explanation

Acceleration results from a change in velocity. Despite the speed remaining constant, velocity is a vector quantity and will change if the car changes direction. In rounding the turn, there is a change in the direction of the velocity, but not in the magnitude. This change in direction causes a non-zero acceleration.

The acceleration will remain equal to the equation for centripetal acceleration:

$a_c=\frac{v^2}{r}$

As long as the magnitude of the velocity and the radius of the turn do not change, the acceleration will remain constant.

What force is required produce an acceleration of $3\frac{m}{s^2}$ on an object of mass ?

Explanation

Newton's second law states that:

We are given the mass of the object and the acceleration. Using these values, we can solve for the necessary force.

$F=5kg*3\frac{m}{s^{2}}$

A constant force acts on an object, causing it to accelerate along a track, when it suddenly breaks in half. What is the ratio of the initial acceleration of the object to the acceleration of one piece after it breaks if the force remains constant after the break?

Explanation

Newton's second law states that:

We are told that the force on the object remains constant, even after it breaks in half. The mass of the broken piece will be equal to half the mass of the total object.

Using these values, we can set up equations for the initial and final accelerations.

$a_1=\frac{F_1}{m_1}$

$a_2=\frac{F_2}{m_2}=\frac{F_1}{\frac{1}{2}m_1}$

$a_2=2\frac{F_1}{m_1}=2a_1$

If the force remains constant while the mass is cut in half, the acceleration of the object will double. The ratio of the new acceleration to the old acceleration will be 2:1. If the question asked for the ratio of the old acceleration to the new one, it would be 1:2.

An ice skater skates on a frictionless surface with a velocity of . If no forces act upon him, what is his velocity after ?

We need to know the skater's mass in order to solve

We need to know the displacement of the skater in order to solve

Explanation

If no forces are acting upon the skater and he is on a frictionless surface, then that means he has no net acceleration.

Mathematically, we can see this relationship from Newton's second law:

$a=0\frac{m}{s^2}$

Presumably the skier has mass, therefore the acceleration must be zero.

If an object moves with a velocity and there is no acceleration, then the velocity remains constant. His velocity after five second will be equal to his initial velocity.

A car moves with a constant velocity of $20\frac{m}{s}$ . What is the net force on the car?

We need to know the mass of the car in order to solve

We need to know the frictional forces in order to solve

Explanation

If an object is moving with constant velocity, then its acceleration must be zero.

$a=\frac{v_2-v_1}{t}$

$v_2=v_1\rightarrow a=\frac{v-v}{t}=\frac{0}{t}=0$

We can then look at Newton's second law. If the acceleration is zero, then the net force must also be zero.

This means that the gravitational force and normal force cancel out, and the propulsion force of the car cancels out the force of friction. Forces may still be acting in respective directions, but the net sum of these forces is zero.

Two dogs are pulling on a bone in opposite directions. If the bone does not move, what conclusions can be drawn?

The dogs are pulling with equal force, but in opposite directions

We need to know the mass of the bone to draw any conclusions

We need to know the weight of the dogs in order to draw any conclusions

The two forces are equal in size and going in the same direction

We need to know the acceleration on the bone in order to draw any conclusions

Explanation

If the bone does not move, then we know that the resultant acceleration on it is zero. That means that the net force must also equal zero.

In other words, the sum of the two forces acting on the bone must be zero.

$F_{net}=F_1+F_2$

Since the forces are pulling in opposite directions, one force must be in the negative direction.

From here, it's simple manipulation to see that the forces are equal.

The forces are equal in size, but going in opposite directions.

How much force is required to move a filing cabinet ?

We need to know the coefficient of friction between the cabinet and the floor

We need to know the final velocity of the cabinet

Explanation

There is insufficient information to solve. Force is the product of mass and acceleration. While we are given the mass, we are not given an acceleration.

If we assume that we are looking for the minimum force required to move the cabinet, then the force would be equal to the force of friction.

Substitute the equations for frictional force and Newton's second law.

$ma=-(\mu F_N)$

Normal force is equal to the force of gravity.

$ma=-\mu (mg)$

The masses cancel out and we know the acceleration due to gravity is constant.

$a=-\mu (g)$

This equation is unsolvable as we do not know $\mu$ , the coefficient of friction between the cabinet and the floor. We cannot find the acceleration of the cabinet, meaning we cannot find the force.

Lance pushes a crate of mass with newtons of force. What is the resultant acceleration?

$\frac{N}{m}$

$\frac{m}{N}$

Explanation

The formula for force is Newton's second law:

We are told in the question to use for the mass and for the force.

Now we can isolate the acceleration.

$\frac{N}{m}=a$

This also makes sense from a units perspective. Units for force are Newtons, which can be written as:

$1N=1\frac{kg\cdot m}{s^2}$

In our equation, we can see that Newtons are divided by mass:

$\frac{N}{m}=\frac{\frac{kg\cdot m}{s^2}}{kg}=\frac{m}{s^2}$

This would result in the units for acceleration.

A crate slides along a frictionless surface. If it maintains a constant velocity of $3\frac{m}{s}$ , what is the net force on the object?

Explanation

Newton's second law states that . We know the mass, but we need to calculate the acceleration.

Acceleration is the change in velocity per unit time.

$a=\frac{v_2-v_1}{t}$

Since the velocity does not change from one moment to the next, then there must be no net acceleration on the object.

$a=\frac{3\frac{m}{s}-3\frac{m}{s}}{t}=\frac{0\frac{m}{s}}{t}$

$a=0\frac{m}{s^2}$

Returning to Newton's second law, we can see that if there is no acceleration, then there is no net force.

$F=7kg*0\frac{m}{s^2}$

A ball begins to roll with a velocity of . If no outside forces act upon it, what will be its velocity in ?

$\frac{v}{10}$

Explanation

If there are no forces acting upon the object, then there is no acceleration. If there is no acceleration, then the object will move with a constant velocity.

Mathematically, we can look at Newton's second law and the formula for acceleration.