A hallway display of energy is constructed in which several people pull on a rope that lifts a block 1.15 m. The display indicates that 0.95 J of work is done. What is the mass of the block?
Walk through would be great
To find the mass of the block, you'll need to use the concept of work and gravitational potential energy. Here's a step-by-step walkthrough:
1. Start by understanding the relationship between work (W), force (F), and distance (d). The formula is: W = F * d * cos(θ), where θ is the angle between the direction of force and the direction of motion.
2. In this scenario, the work done is given as 0.95 J.
3. The distance lifted is given as 1.15 m.
4. Now, recall that work is done against gravity when a mass is lifted. The work done against gravity is equal to the change in gravitational potential energy. The formula for gravitational potential energy is: PE = m * g * h, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
5. In this case, the work done against gravity is equal to the change in gravitational potential energy. So, the work done (0.95 J) is equal to the change in gravitational potential energy, which is m * g * h.
6. Rearrange the equation to solve for the mass (m): m = W / (g * h).
7. Plug in the values: W = 0.95 J, g = 9.8 m/s^2, and h = 1.15 m.
8. Calculate the mass: m = 0.95 J / (9.8 m/s^2 * 1.15 m).
9. Solve the equation: m = 0.95 J / 11.27 kg*m/s^2.
10. Simplify the units: kg*m/s^2 is equivalent to a Newton (N), so m = 0.95 N / 11.27 N.
11. The units cancel out, leaving the mass in kilograms (kg).
12. Calculate the mass: m ≈ 0.084 kg.
Therefore, the mass of the block is approximately 0.084 kg.