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Forces and Motion (College)

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Forces and Motion

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:
  1. 4.75
  2. 5.54
  3. 3.33
  4. 2.31
  5. 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]?
  1. 10 N
  2. 12 N
  3. 13 N
  4. 14 N
  5. 16 N
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?
  1. 6 Joules
  2. 9 Joules
  3. 10 Joules
  4. 12 Joules
  5. 17 Joules
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?
  1. 10 m
  2. 20 m
  3. 40 m
  4. 60 m
  5. 80 m
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
  1. moving with constant speed along a circle.
  2. moving with varying speed along a circle.
  3. moving with constant acceleration along a straight line.
  4. moving along a parabola.
  5. oscillating back and forth along a straight line.
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.)
  1. [math]-a+2bx[/math]
  2. [math]a-2bx[/math]
  3. [math]-ax^2/2+bx^3/3[/math]
  4. [math]ax^2/2-bx^3/3[/math]
  5. [math]-ax^2/2+bx^3/3+c[/math]
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 planet’s surface if the projectile is to escape from the planet’s gravitational field?
  1. [math]K=sqrtgR[/math]
  2. [math]K=mgR[/math]
  3. [math]K=mg/R[/math]
  4. [math]K=msqrt(g/R)[/math]
  5. [math]K=gR[/math]
The sum of all the external forces on a system of particles is zero. Which of the
following must be true of the system?
  1. The total mechanical energy is constant.
  2. The total potential energy is constant.
  3. The total kinetic energy is constant.
  4. The total linear momentum is constant.
  5. It is in static equilibrium.
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
  1. 4 m/s
  2. 10 m/s
  3. 13 m/s
  4. 16 m/s
  5. 21 m/s
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?
  1. the velocity of the ball is negative and the acceleration is negative
  2. the velocity of the ball is negative and the acceleration is positive
  3. the velocity of the ball is positive and the acceleration is negative
  4. the velocity of the ball is positive and the acceleration is positive
  5. the velocity of the ball is zero and the acceleration is negative
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