Question

which of the following statements are impossible? choose all that apply. jill exerted 80 n of force due west on a cart. as a direct result, the cart exerted 80 n of force due west upon jill. a pencil exerts a smaller gravitational force upon neptune than neptune exerts upon it. the moving motorcycle had 1331 kg·m/s of momentum. the truck had 4407 j of ke and 764 kg·m/s of momentum. a box had an acceleration of 4705 m/s2 while a net force of 181 n acted on it. a ball moving in a circle had 0 n of net force acting on it. at a certain point in time, the total energy of a closed system is observed to be 370 j. which one of the following statements is true? three hours later the energy of the system is 185 j. some of the energy must be potential. seven hours later the energy of the system is 740 j. seven hours later the energy of the system is 370 j. all of the energy must be kinetic energy.

Explanation:

Step1: Analyze the first problem

Jill exerted 80 N of force due west on a cart. As a direct result, the cart exerted 80 N of force due west upon Jill.

According to Newton's third law, when Jill exerts a force on the cart, the cart exerts an equal and opposite force on Jill. So the direction of the force exerted by the cart on Jill should be due east. This statement is impossible.

A pencil exerts a smaller gravitational force upon Neptune than Neptune exerts upon it.

According to Newton's law of gravitation \(F = G\frac{m_1m_2}{r^2}\), the gravitational force between two objects is mutual. The force that the pencil exerts on Neptune is equal in magnitude to the force that Neptune exerts on the pencil. This statement is impossible.

The moving motorcycle had 1331 kg·m/s of momentum.

Momentum \(p=mv\). Since a motorcycle has mass \(m>0\) and can have a non - zero velocity \(v\), it is possible for a motorcycle to have a momentum of \(1331\space kg\cdot m/s\).

The truck had 4407 J of KE and 764 kg·m/s of momentum.

We know that \(KE=\frac{p^{2}}{2m}\) and \(p = mv\). If \(p = 764\space kg\cdot m/s\), then \(m=\frac{p}{v}\). Substituting into the kinetic energy formula \(KE=\frac{p^{2}}{2m}=\frac{pv}{2}\). We can find a non - negative value of \(v\) (since \(v=\frac{2KE}{p}\), \(v=\frac{2\times4407}{764}\approx11.5\space m/s\)) and \(m=\frac{p}{v}=\frac{764}{11.5}\approx66.4\space kg\). So it is possible.

A box had an acceleration of 4705 m/s² while a net force of 181 N acted on it.

From Newton's second law \(F = ma\), then \(m=\frac{F}{a}\). Substituting \(F = 181\space N\) and \(a=4705\space m/s^{2}\), we get \(m=\frac{181}{4705}\approx0.0385\space kg\). Since mass \(m>0\), it is possible.

A ball moving in a circle had 0 N of net force acting on it.

For a ball moving in a circle, there must be a centripetal force \(F_c=\frac{mv^{2}}{r}\) (where \(m\) is the mass of the ball, \(v\) is the tangential speed, and \(r\) is the radius of the circular path). If \(F_c = 0\), then \(v = 0\) (assuming \(m
eq0\) and \(r
eq0\)), and the ball is not moving in a circle. So this statement is impossible.

Step2: Analyze the second problem

According to the law of conservation of energy for a closed system, the total energy of a closed system is conserved. That is, \(E_{total}\) remains constant over time.

Three hours later the energy of the system is 185 J.

Since the system is closed, energy should be conserved. If the initial energy is \(370\space J\), this is impossible.

Some of the energy must be potential.

The total energy is the sum of kinetic and potential energy (\(E = KE+PE\)). But we cannot say that some of the energy must be potential. It could be all kinetic (if \(PE = 0\)) or a combination.

Seven hours later the energy of the system is 740 J.

Since the system is closed, energy should be conserved. If the initial energy is \(370\space J\), this is impossible.

Seven hours later the energy of the system is 370 J.

By the law of conservation of energy for a closed system, the total energy of a closed system is conserved. So this is possible.

All of the energy must be kinetic energy.

The total energy is the sum of kinetic and potential energy (\(E = KE + PE\)). But we cannot say that all of the energy must be kinetic. It could be a combination of kinetic and potential.

Answer:

For the first problem:

• Jill exerted 80 N of force due west on a cart. As a direct result, the cart exerted 80 N of force due west upon Jill.
• A pencil exerts a smaller gravitational force upon Neptune than Neptune exerts upon it.
• A ball moving in a circle had 0 N of net force acting on it.

For the second problem: Seven hours later the energy of the system is 370 J.