Can anyone figure this out?
A cable with 25.0N of tension pulls straight up on a 1.10kg block that is initially at rest.
What is the block's speed after being lifted 2.30m ? Solve this problem using work and energy.
To find the block's speed after being lifted, we can use the principles of work and energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the block is equal to the change in its gravitational potential energy.
First, let's calculate the work done on the block. The work done is equal to the force applied multiplied by the displacement. In this case, the force is the tension in the cable, which is 25.0N, and the displacement is the vertical distance the block is lifted, which is 2.30m.
Work (W) = Force (F) × Displacement (d)
W = 25.0N × 2.30m
Next, we need to calculate the change in gravitational potential energy. The change in gravitational potential energy is equal to the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2) multiplied by the change in height.
Change in Potential Energy (ΔPE) = mass (m) × gravity (g) × change in height (h)
ΔPE = 1.10kg × 9.8 m/s^2 × 2.30m
According to the work-energy principle, the work done on the block (W) is equal to the change in potential energy (ΔPE). So we can set up an equation:
W = ΔPE
25.0N × 2.30m = 1.10kg × 9.8 m/s^2 × 2.30m
Now, we can solve for the speed (v) of the block using the equation for kinetic energy:
Kinetic Energy (KE) = 0.5 × mass (m) × velocity (v)^2
The change in kinetic energy is equal to the work done on the object:
ΔKE = W
0.5 × 1.10kg × v^2 = 25.0N × 2.30m
From here, we can solve for the speed (v) by rearranging the equation:
v^2 = (25.0N × 2.30m) / (0.5 × 1.10kg)
Take the square root of both sides of the equation to find the speed (v):
v = √[(25.0N × 2.30m) / (0.5 × 1.10kg)]
Calculating this expression should give you the block's speed after being lifted 2.30m.