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- Homework Statement
- Consider a cylinder c of mass m = 10 kg and radius r 0.07 m rolls without slipping on slope H as shown below. The string is wrapped around cylinder c and does not stretch and does not slip on the cylinder. Assume the pulley to be massless.

(a) Explain very briefly why when the mass m = 2 kg moves by one meter, cylinder c moves vertically by 0.25m.

(b) Calculate the magnitude of a cm of cylinder c.

- Relevant Equations
- τ = I α

a = r α

Resolving the weight of the cylinder c, i get Mgcosθ (-y) and Mgsinθ (-x)

mgsinθ - Fs - T = ma ---(1) (where Fs is frictional force and T is tension)

τ = I α (where τ is torque and α is angular acceleration)

torque is produced by both tension and frictional force

(T-Fs) * r = 0.5 m r^2 α

a = r α

T- Fs = 0.5 m a

Fs = T - 0.5ma --- (2)

sub (2) into (1)

mgsinθ - T + 0.5ma -T = ma

mgsinθ -2T = 0.5ma

mgsingθ - 2(mg) = 0.5ma (where m in T is 2kg)

after putting in numbers,

a = 1.96m/s^2

ans: 0.426m/s^2

mgsinθ - Fs - T = ma ---(1) (where Fs is frictional force and T is tension)

τ = I α (where τ is torque and α is angular acceleration)

torque is produced by both tension and frictional force

(T-Fs) * r = 0.5 m r^2 α

a = r α

T- Fs = 0.5 m a

Fs = T - 0.5ma --- (2)

sub (2) into (1)

mgsinθ - T + 0.5ma -T = ma

mgsinθ -2T = 0.5ma

mgsingθ - 2(mg) = 0.5ma (where m in T is 2kg)

after putting in numbers,

a = 1.96m/s^2

ans: 0.426m/s^2