This is a simple cart driven by a friction drive system, where the motor comes i

Question

This is a simple cart driven by a friction drive system, where the motor comes in direct contact with the wheel, transfering the same angular velocity. I need to calculate the maimum pushing force and the velocity of the cart using the following Free body diagram. The car travels to the right. I made the graph myself so there may be minor errors in the direction of arrows. (if so please correct me). Feel free to define parameters and add any variables if needed, as long as you explain what they represent.

PS: Assumptions friction between the wheel and the ground is neglected, and that the wheel and motor are always in perfect contact with each other.actual measured values of the cart's pushing force came out to be about 3N, and the average velocity was about 11 inches/sec.

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This is a simple cart driven by a friction drive system, where the motor comes in direct contact with the wheel, transfering the same angular velocity. I need to calculate the maimum pushing force and the velocity of the cart using the following Free body diagram. The car travels to the right. I made the graph myself so there may be minor errors in the direction of arrows. (if so please correct me). Feel free to define parameters and add any variables if needed, as long as you explain what they represent. PS: Assumptions friction between the wheel and the ground is neglected, and that the wheel and motor are always in perfect contact with each other.actual measured values of the cart's pushing force came out to be about 3N, and the average velocity was about 11 inches/sec.

Explanation / Answer

For motor:

R = F_spring

Torque T = I_motor*alpha_motor...........where alpha = angular acceleration and I = Inertia of motor shaft

T = f*r_motor............1

where f = friction force

Assuming no slip between motor and wheel, tangential velocity v = r_motor*w_motor = R_w*w_wheel

Here..w = angular velocity.

It is given that w_motor = w_wheel.

Therefore, we get that r_motor = R_w

Thus, T = f*R_w = I_motor*alpha_motor

For Wheel:

Torque T = f*R_w........2

Mg + R*Cos theta = N + f*sin theta............where theta = angle between direction of R and vertical.

From eqn 1, f = T / r_motor

Therefore, Pushing force F_push = f = T / r_motor

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