I need help with these two questions if someone can help me please? Thank you!

Question

A top has a peg along its axis with a lightweight string wrapped around it. As shown below, the end of the string is pulled with a constant tension force F = 4.32 N, causing the string to unwind from the peg without slipping. The top has a moment of inertia of 4.30 ✕ 10−4 kg · m2. It is initially at rest and is free to rotate about the stationary axis AA'. What is the top's angular speed (in rad/s) after 70.0 cm of string has unwound from the peg?

 _____ rad/s

A hanging weight with a mass of m1 = 0.375 kg, is attached by a string to a block with mass m2 = 0.865 kg. The string goes over a pulley with a mass of M = 0.350 kg, and the pulley is a hollow cylinder with an inner radius of R1 = 0.0200 m and an outer radius of R2 = 0.0300 m. The coefficient of kinetic friction between the block and the table is μk = 0.250. The block is moving with a velocity of vi = 0.820 m/s toward the pulley.



A. Using energy methods, find the speed of the block (in m/s) after it has moved a distance of 0.700 m away from the initial position shown.

 _____m/s

B. What is the angular speed of the pulley (in rad/s) after the block has moved this distance?

 _____ rad/s

Answer 1

Use the formula τ = Iα and solve for angular acceleration.

Next use the equation:

ω² = ω₀² + 2αθ = 2αθ

Change the 70cm of string into radians of string wrapped around the peg and solve for ω.