Work
Energy
Power
Sports
Potpourri
100
The x component of a force on a particle is given by F(x)=3/(1+3x). How much work is done by the force in moving the particle from x=0 to x=2m?
W=ln(7)
100
A mass of 3kg is shot straight upwards from a spring compressed by 4m with a spring constant of 100N/m. It flies up and then crashes back into the ground. How long is the mass in the air?
t=4.71s
100
A 2kg mass is accelerated from a speed 3m/s to a speed of 4m/s in a time 14 seconds. What was the power required to accomplish this?
P=1/2 W
100
The potential energy of a baseball is given by U(x)=4/(1+3x). What is the magnitude and direction of the force on the particle at x=1m?
F=3/4 N to the right
100
The (x,y) components of a force on a particle is given by (-5,2) and the displacement of the particle is given by (3,10). What is the amount of work done on the particle by the force?
W=+5J
200
The (x,y) components of a constant force in Newtons are given by (-2,6). What is the amount of work done on a 3kg particle that moves along the x axis from x=-3m to x=-5m?
W=+4J
200
Mass A has a mass M and is dropped from height H. Mass B has a mass M/2 and is dropped from height 4H. What is the ratio of the kinetic energy of A to the kinetic energy of B right before striking the ground?
1/8
200
A 4kg mass is at rest and 2m above the ground. It is then lifted and accelerated to a point 5m above the ground and moving with a speed 4m/s in a time 9.35s. What is the power required to accomplish this?
16W
200
A conservative force on a soccer ball is given by F(x)=-8x3 + 4. What is the potential energy associated with this force as a function of x? Assume that the potential energy is zero at x=0.
U(x)=-2x4 -4x
200
The (x,y) components of the net force on a 2kg particle is given by (2,6) and the displacement of the particle is given by (-4,1). The particle started with a speed of 3m/s. What speed does the particle end with?
√ 7
300
What is the final speed of a 4kg mass that start from rest and experiences a force in the y direction given by F(y)=3y, and moves from y=2m to y=4m?
v=3m/s
300
Spring A has a spring constant K and is compressed a distance D. Spring B has a spring constant 8K and is compressed a distance D/2. What is the ratio of the potential energy of spring A compared to spring B?
1/2
300
The power used by an engine is given by the formula P(t)=4e-t/3. How much energy is used by the engine between t=0 and t=6 seconds?
E=10.4 J
300
A basketball of mass M is dropped from a height H. It then compresses a spring of spring constant K on the ground which stops the ball. In terms of given quantities and fundamental constants, what is the amount that the basketball compresses the spring?
√(2MgH/K)
300
A box of mass M is dragged a distance D across the floor with a rope with tension T directed at an angle θ above the horizontal. The coefficient of kinetic friction is μ. What is the work done by the tension force, the normal force, gravity, and the frictional force in terms of given quantities and fundamental constants?
TDcosθ
0
0
μ(Mg-Tsinθ)D
400
The components of the net force on a 2kg particle are given by (-2x, 0). The particle starts at the origin with a velocity 10m/s in the -x direction. What is the speed of the particle when it reaches x=-5m?
√ 75
400
A 4kg mass hangs at rest vertically from a string of length 2m. The mass is lifted so the string makes and angle of 30o with respect to a vertical line. The mass is released and swings freely. If the speed of the mass when it swings through its lowest point is 1.5m/s, how much energy was lost to work done by dissipative forces?
E=6J
400
The energy used by a circuit is given by E(t)=5sin(3t). What is the maximum instantaneous power that must be supplied to the circuit?
P=15W
400
Hockey puck A of mass M is moving with speed u. Hockey puck B of mass 5M is moving with speed u/5. If both pucks run into identical springs, what is the ratio of the amount that puck A compresses its spring, compared to the amount that puck B compresses its spring?
√ 5
400
The potential energy of the net force on a 10kg particle is given by U(x)=5x where x is in meters. What is the ratio of the acceleration of the mass at x=1m compared to the acceleration of the mass at x=2m?
1
500
The components of a force on a 3kg particle is given by (3/x, 12y2). The particle moves from the (x,y) position (-2m, -1m) to (-2m, 3m). How much work did the force do on the particle?
W=112 J
500
The potential energy of a 12kg mass is in Joules is given by U(x)=4x2. What is the size and direction of the acceleration of the mass if it is at x=2m and is moving with a velocity of 12m/s in the +x direction?
a=-4/3 m/s2
500
The power used by a circuit is given by P(t)=3sin(2t). How much energy must be supplied to the circuit between t=0 and t=π/2?
E=3J
500
The position formula x(t)=6sin(t/3) gives the position in meters of a 0.15kg baseball. What is the ratio of the kinetic energy at t=π compared to the kinetic energy at t=0sec?
1/4
500
A mass M starts from rest on the top of a building of height H and is launched off the building by a spring with spring constant K that was compressed by a distance D. How fast is the mass going when it hits the ground in terms of M, H, K, D, and fundamental constants?
√(2gH+KD2/M)
M
e
n
u