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The 143-kg uniform crate rests on the 10-kg cart. The coefficient of static friction between the crate and cart is [tex]\mu_s = 0.2[/tex].

**Part A:**
Determine the maximum magnitude of the force \(P\) that can be applied to the handle without causing the crate to slip or tip on the cart. Express your answer to three significant figures and include the appropriate units.

Answer :

To prevent the crate from slipping or tipping, the force P applied to the handle must not exceed the maximum static friction force. Therefore, the maximum magnitude of force P is 299.88 N.

To determine the maximum magnitude of the force P that can be applied to the handle without causing the crate to slip or tip on the cart, we need to consider both the static friction between the crate and the cart and the possibility of tipping.

The maximum static friction force can be calculated using the formula:

F_friction = μs * N

where μs is the coefficient of static friction and N is the normal force.

The normal force N is equal to the weight of the crate plus the weight of the cart. The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity (g).

  • Weight of crate = mass of crate * g

Weight of crate = 143 kg * 9.8 m/s^2

Weight of crate = 1401.4 N

  • Weight of cart = mass of cart * g

Weight of cart = 10 kg * 9.8 m/s^2

Weight of cart = 98 N

  • Normal force N = Weight of crate + Weight of cart

Normal force N = 1401.4 N + 98 N

Normal force N = 1499.4 N

  • Now we can calculate the maximum static friction force:

F_friction = μs * N

F_friction = 0.2 * 1499.4 N

F_friction = 299.88 N

To prevent the crate from slipping or tipping, the force P applied to the handle must not exceed the maximum static friction force. Therefore, the maximum magnitude of force P is 299.88 N.

An object's frictional force is caused by static friction when the object is not moving. This type of friction is referred to as static friction. It's critical since, without it, the object would continue to slip.

To know more about static friction, visit the link : https://brainly.com/question/13680415

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