A cart on a surface with a coefficient of friction of 0.20 is attached to an overhanging weight with a frictionless pulley. The cart has a mass of 2.5 kg while the overhanging weight has a mass of 1.0 kg.
What is the acceleration of the cart?
What is the tension in the cord used to pull the cart?
Please help ASAP, thanks.
well, look at the net accelerating force.
Net accelerating force=totalmass*a
1kg*9.8-.2*2.5*9.8=(3.5kg)a
solve for acceleration.
Tension? Look at the tension pulling the cart: Tension= ma+friction=2.5*a+.2*2.5*9.8
check all that against your force diagram. If you wish, compare it with the tension at the other end holding the falling weight: T=(mg-ma)=
T=9.8N-1*a
To find the acceleration of the cart, we can use Newton's second law of motion. This law states that the net force acting on an object is equal to the product of its mass and acceleration.
Step 1: Find the net force acting on the cart.
The net force is the difference between the force pulling the cart and the force of friction opposing its motion. In this case, the force pulling the cart is the tension in the cord, and the force of friction can be calculated using the coefficient of friction and the normal force.
Step 2: Find the force of friction.
The force of friction is given by the equation: force of friction = coefficient of friction * normal force.
The normal force in this case is equal to the weight of the cart, which is calculated by multiplying the mass of the cart by the acceleration due to gravity (9.8 m/s^2).
Step 3: Find the tension in the cord.
The tension in the cord is the force pulling the cart. Since the cart is attached to an overhanging weight with a frictionless pulley, the tension in the cord is the weight of the overhanging weight (mass of the overhanging weight * acceleration due to gravity).
Now, let's calculate the acceleration and tension:
Step 1: Find the net force acting on the cart.
Net force = Tension - Force of friction
Step 2: Find the force of friction.
Force of friction = coefficient of friction * normal force
Normal force = mass of cart * acceleration due to gravity
Step 3: Find the tension in the cord.
Tension = mass of overhanging weight * acceleration due to gravity
Now we can substitute the values into the equations and solve for the acceleration and tension.
Acceleration:
Net force = mass of cart * acceleration
Tension - force of friction = mass of cart * acceleration
Tension:
Tension = mass of overhanging weight * acceleration due to gravity
By solving these equations simultaneously, we can find the values of acceleration and tension.