A yoyo of mass m= 2 kg and moment of inertia I_cm= 0.09 kg m consists of two solid disks of radius R= 0.3 m, connected by a central spindle of radius r= 0.225 m and negligible mass. A light string is coiled around the central spindle. The yoyo is placed upright on a flat rough surface and the string is pulled with a horizontal force F= 24 N, and the yoyo rolls without slipping
a)What is the x-component of the acceleration of the center of mass of the yoyo? (in m/s )
b)) What is the x-component of the friction force? (in N)
have you got the answer?
To solve this problem, we need to use Newton's second law and the rotational dynamics of the yoyo. We'll break down the problem into two parts: the linear motion of the center of mass and the rotational motion of the yoyo.
Let's first consider the linear motion of the center of mass:
a) As per Newton's second law, the net force acting on the yoyo in the x-direction is equal to the product of the mass and acceleration: F_net = m * a_cm.
In this case, the only horizontally applied force is F, so the net force is equal to the applied force minus the friction force: F_net = F - f_friction.
Since the yoyo is rolling without slipping, the friction force can be determined using the relation: f_friction = μ * N, where μ is the coefficient of friction and N is the normal force.
The normal force N is equal to the weight of the yoyo, which in this case is given by the product of mass m and acceleration due to gravity g: N = m * g.
Substituting these values into the equation F_net = F - f_friction, we get: F - μ * m * g = m * a_cm.
Now, we can solve for the x-component of the acceleration of the center of mass (a_cm):
a_cm = (F - μ * m * g) / m.
b) To calculate the x-component of the friction force, we need to know the coefficient of friction (μ). Unfortunately, the coefficient of friction is not provided in the given information. Therefore, it is not possible to determine the exact value of the friction force without this information.