Consider the system of two crates shown below, which are tethered to each other by a massless string, which runs over a massless frictionless pulley. Crate 1's mass is m1 35.0 kg and crate 2's mass is m2 = 60.0 kg. Suppose crate 1 slides L = 22.0 m up the ramp and starts from rest. %3D The coefficient of kinetic friction between crate 1 and the ramp is Hk = 0.205. Determine the %3D speed of crate 1 after slidingL = 22.0 m up the ramp. Let 0 = 31.7°.

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**Problem Statement:**

Consider the system of two crates shown below, which are tethered to each other by a massless string, which runs over a massless frictionless pulley. Crate 1’s mass is \( m_1 = 35.0 \, \text{kg} \) and crate 2’s mass is \( m_2 = 60.0 \, \text{kg} \). Suppose crate 1 slides \( L = 22.0 \, \text{m} \) up the ramp and starts from rest. The coefficient of kinetic friction between crate 1 and the ramp is \( \mu_k = 0.205 \). Determine the speed of crate 1 after sliding \( L = 22.0 \, \text{m} \) up the ramp. Let \( \theta = 31.7^\circ \).

**Diagram Description:**

- The diagram depicts a ramp inclined at an angle \( \theta = 31.7^\circ \).
- Crate 1 with mass \( m_1 \) is on the inclined ramp.
- Crate 2 with mass \( m_2 \) hangs vertically off the edge of the ramp, attached to crate 1 via a pulley system.
- The ramp shows the direction of motion for crate 1 with an arrow pointing upwards along the ramp.
- The distance \( L = 22.0 \, \text{m} \) is marked along the ramp, indicating the length crate 1 travels.
- A pulley is illustrated at the top of the ramp, connected to both crates.
  
**Objective:**

Calculate the speed of crate 1 after it has slid 22.0 meters up the ramp, taking into account the effects of kinetic friction and gravity.
Transcribed Image Text:**Problem Statement:** Consider the system of two crates shown below, which are tethered to each other by a massless string, which runs over a massless frictionless pulley. Crate 1’s mass is \( m_1 = 35.0 \, \text{kg} \) and crate 2’s mass is \( m_2 = 60.0 \, \text{kg} \). Suppose crate 1 slides \( L = 22.0 \, \text{m} \) up the ramp and starts from rest. The coefficient of kinetic friction between crate 1 and the ramp is \( \mu_k = 0.205 \). Determine the speed of crate 1 after sliding \( L = 22.0 \, \text{m} \) up the ramp. Let \( \theta = 31.7^\circ \). **Diagram Description:** - The diagram depicts a ramp inclined at an angle \( \theta = 31.7^\circ \). - Crate 1 with mass \( m_1 \) is on the inclined ramp. - Crate 2 with mass \( m_2 \) hangs vertically off the edge of the ramp, attached to crate 1 via a pulley system. - The ramp shows the direction of motion for crate 1 with an arrow pointing upwards along the ramp. - The distance \( L = 22.0 \, \text{m} \) is marked along the ramp, indicating the length crate 1 travels. - A pulley is illustrated at the top of the ramp, connected to both crates. **Objective:** Calculate the speed of crate 1 after it has slid 22.0 meters up the ramp, taking into account the effects of kinetic friction and gravity.
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