A 30kg block sits on a ramp, with Θ=47. The ramp is 13m off the ground at the tallest point. If the block slides in the presence of friction, with μ=0.1, how fast is the block moving when it hits the bottom of the ramp?
Please indicate which equation you use, what variable corresponds to each number, and how you got the number that goes with the variable.
Thanks!
I am beginning see your posts as pure answer grazing, which does not reflect positively on you. You can do better than that.
Her, I would find the answer from energy considerations:
First, the force of friction: mg*mu*cosTheta
then, find the distance down the ramp: 13/sinTheta
KE at bottom=PE at top - frictionwork
1/2 mvf^2=mgh-forcefriction*distance
solve for vf
What makes you think I just want answers. I am here to learn and simply showing me how to set up the problem is enough. Your answer was helpful but you don't have to be mean.
To find the speed at which the block hits the bottom of the ramp, we can use the conservation of mechanical energy. The equation for this situation is:
E_initial = E_final
where E_initial is the initial mechanical energy of the block, and E_final is the final mechanical energy of the block at the bottom of the ramp.
The initial mechanical energy includes potential energy and kinetic energy, while the final mechanical energy only includes kinetic energy. Let's break it down step by step:
1. Find the initial mechanical energy (E_initial):
- The block is initially at a height of 13m from the ground, so the potential energy is given by:
Potential energy = mass * gravity * height
Potential energy = 30kg * 9.8m/s^2 * 13m
- Since the block is initially at rest, the initial kinetic energy is zero.
- Therefore, E_initial = Potential energy + 0 (kinetic energy)
E_initial = 30kg * 9.8m/s^2 * 13m
2. Find the final mechanical energy (E_final):
- At the bottom of the ramp, the block has reached its maximum speed, so all of the initial potential energy has been converted to kinetic energy.
E_final = 0 (potential energy) + 1/2 * mass * speed^2
3. Set up the equation:
Since energy is conserved, we can equate the initial energy to the final energy:
E_initial = E_final
Now, substitute the values we found earlier:
30kg * 9.8m/s^2 * 13m = 1/2 * 30kg * speed^2
4. Solve for speed:
Rearrange the equation and solve for speed:
speed^2 = (30kg * 9.8m/s^2 * 13m) / (1/2 * 30kg)
speed^2 = 9.8m/s^2 * 13m / (1/2)
speed^2 = 9.8m/s^2 * 13m * 2
speed^2 = 254.8m^2/s^2
Take the square root of both sides to find the speed:
speed = √(254.8m^2/s^2)
speed ≈ 15.96 m/s
Therefore, the block will be moving at approximately 15.96 m/s when it hits the bottom of the ramp.