# Forces and Motion

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## Forces and Motion Answer Key

1.

A cannon fires a projectile into the air at an angle of [math]60deg[/math]above the horizontal. The projectile falls back on the ground at a distance d from the cannon and its maximum height is h. Ratio d/h is equal to:

- 4.75
- 5.54
- 3.33
- 2.31
- 2

2.

An 1kg object moves along the x-axis according to the function [math]x(t)=mt^3+nt^2+pt+q[/math], where m,n,p and q are real numbers. If the magnitude of the net force acting at [math]t_1=1s[/math]is 4 Newtons and at [math]t_2=2s[/math]is 10 Newtons, what is the magnitude of the force at [math]t_3=3s[/math]?

- 10 N
- 12 N
- 13 N
- 14 N
- 16 N

3.

A force F acting on an object is given by the expression [math]F(s)=(7s^(3/4)+5)[/math] Newtons, where s is the position of the object in meters. What is the work done by the force F between s = 0m and s = 1m?

- 6 Joules
- 9 Joules
- 10 Joules
- 12 Joules
- 17 Joules

4.

On a certain planet, a ball is thrown upward with a kinetic energy of 100 J and an angle of elevation of [math]45deg[/math]. If the ball has a kinetic energy of 75 J at a height of 10 m, what is the maximum height of its trajectory?

- 10 m
- 20 m
- 40 m
- 60 m
- 80 m

5.

If a particle moves in a plane so that its position is described by the functions

[math]x=Acosomegat[/math] and [math]y=Asinomegat[/math], the particle is

[math]x=Acosomegat[/math] and [math]y=Asinomegat[/math], the particle is

- moving with constant speed along a circle.
- moving with varying speed along a circle.
- moving with constant acceleration along a straight line.
- moving along a parabola.
- oscillating back and forth along a straight line.

6.

A certain spring has a sectoring force that obeys the equation [math]F(x)=-ax+bx^2[/math]. Which of the following is the equation for the potential energy as a function of position? (Set the potential energy equal to zero at the equilibrium point of the spring, x=0.)

- [math]-a+2bx[/math]
- [math]a-2bx[/math]
- [math]-ax^2/2+bx^3/3[/math]
- [math]ax^2/2-bx^3/3[/math]
- [math]-ax^2/2+bx^3/3+c[/math]

7.

Let [math]g[/math] be the acceleration due to gravity at the surface of a planet of radius [math]R[/math]. Which of the following is a dimensionally correct formula for the minimum kinetic energy [math]K[/math] that a projectile of mass [math]m[/math] must have at the planetâ€™s surface if the projectile is to escape from the planetâ€™s gravitational field?

- [math]K=sqrtgR[/math]
- [math]K=mgR[/math]
- [math]K=mg/R[/math]
- [math]K=msqrt(g/R)[/math]
- [math]K=gR[/math]

8.

The sum of all the external forces on a system of particles is zero. Which of the

following must be true of the system?

following must be true of the system?

- The total mechanical energy is constant.
- The total potential energy is constant.
- The total kinetic energy is constant.
- The total linear momentum is constant.
- It is in static equilibrium.

9.

A descending elevator of mass 1,000 kg is uniformly decelerated to rest over a distance of 8 m by a cable in which the tension is 11,000 N. The initial speed of the elevator is most nearly

- 4 m/s
- 10 m/s
- 13 m/s
- 16 m/s
- 21 m/s

10.

A football is tossed up into the air in the +y direction. Which of the following is true at the point where the football reaches the ground?

- the velocity of the ball is negative and the acceleration is negative
- the velocity of the ball is negative and the acceleration is positive
- the velocity of the ball is positive and the acceleration is negative
- the velocity of the ball is positive and the acceleration is positive
- the velocity of the ball is zero and the acceleration is negative

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