A cart initially at rest on a horizontal floor requires a 365N horizontal force to set it in motion. We know that the coefficient of static friction is 0.64. What is the mass of the cart?
forcetomove=mu*mg
solve for mass m
To find the mass of the cart, we need to apply Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force required to set the cart in motion is the force of static friction. The formula for static friction is given by:
fs = μs * N
where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force.
The normal force N is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the cart, since it is at rest on a horizontal floor. The formula for the weight of an object is given by:
W = m * g
where W is the weight of the object, m is the mass of the object, and g is the acceleration due to gravity.
Since the cart is at rest, the force of static friction is equal to the force required to set it in motion:
fs = 365 N
Now, we can solve the equation:
fs = μs * N
365 N = 0.64 * N
Now, we can solve for N:
N = 365 N / 0.64
N ≈ 570.31 N
Since N is equal to the weight of the cart, we can use this value to find the mass of the cart:
N = W = m * g
570.31 N = m * 9.8 m/s^2
Now, we can solve for the mass:
m = 570.31 N / 9.8 m/s^2
m ≈ 58.2 kg
Therefore, the mass of the cart is approximately 58.2 kg.