PHYSICS work/power/energy question

[r3dxP]

8. For each statement, write true or false.
A)only the net force acting on an object can do work.
i think its TRUE.
B)no work is done on a particle that remains at rest.
i think its TRUE.
C)a force that is always perpendicular to the velocity of a particle never does work on the particle.
i think its TRUE.

^ please correct me if I am wrong.. ^ thx.

6. A particle of mass m moves along the x axis. Its position varies with time according to x=2t^3 + 4t^2 where x is in meters and t is in seconds.
B)find the power delivered to the particle at any time t.
?
C)the work done by the force from t=0 to t=11
im guessing i have to integrate the equation 2t^3 + 4t^2 with 11 on top right of the integration sign and 0 on the bottom of the integration sign.
any comment will be hhelpful. thanks in advance!

10. If a ski lift raises 100 passengers averaging 660N in weight to a height of 150m in 60s, at constant speed, what average power is required of the force making the lift?
I got P = W/t = mgh/t = 660N*150m/60s = 1650W = 1.6kW
did i do this right?

 

[Andrew Mason]

8. For each statement, write true or false.
A)only the net force acting on an object can do work.
i think its TRUE.

Think about two equal and opposite forces compressing a volume of gas. The net force is 0. But there is work done ($W=P\Delta V$).

B)no work is done on a particle that remains at rest.
i think its TRUE.

See example above.

C)a force that is always perpendicular to the velocity of a particle never does work on the particle.
i think its TRUE.

True. Since $W = \int \vec{F}\cdot \vec{s} = \int F\cdot \vec{v} dt = \int Fvdt cos\theta$ if $\theta$ is always 90 degrees, then W = 0.

6. A particle of mass m moves along the x axis. Its position varies with time according to x=2t^3 + 4t^2 where x is in meters and t is in seconds.
B)find the power delivered to the particle at any time t.

Use $P = dW/dt = Fds/dt = Fv = mav = m\ddot x \dot x$

C)the work done by the force from t=0 to t=11
im guessing i have to integrate the equation 2t^3 + 4t^2 with 11 on top right of the integration sign and 0 on the bottom of the integration sign.

See suggestion in B)

10. If a ski lift raises 100 passengers averaging 660N in weight to a height of 150m in 60s, at constant speed, what average power is required of the force making the lift?
I got P = W/t = mgh/t = 660N*150m/60s = 1650W = 1.6kW
did i do this right?

The work done in raising 100 passengers is W=mgh where mg = 100*660N and h = 150 m. So the correct answer is 165000 W. or 165 kW.

AM

 

[r3dxP]

Think about two equal and opposite forces compressing a volume of gas. The net force is 0. But there is work done ($W=P\Delta V$).
See example above.
True. Since $W = \int \vec{F}\cdot \vec{s} = \int F\cdot \vec{v} dt = \int Fvdt cos\theta$ if $\theta$ is always 90 degrees, then W = 0.

Use $P = dW/dt = Fds/dt = Fv = mav = m\ddot x \dot x$
See suggestion in B)

The work done in raising 100 passengers is W=mgh where mg = 100*660N and h = 150 m. So the correct answer is 165000 W. or 165 kW.

AM

um.. mg = 660 m^2/s^2.. then multiply this by h=150m. I don't understand how you could put 100 as its mass...

 

[Andrew Mason]

um.. mg = 660 m^2/s^2.. then multiply this by h=150m. I don't understand how you could put 100 as its mass...

660 N is the weight of one person (average). There are 100 people. So the total weight is 100*660.

AM