consider a yo-yo (of mass M and outer radius R), where the string is being pulled with a force of magnitude F(F<Mg) at an angle theta. the radius of the inner axis is r(so that<R). Assume that the angle ranges from 0 to pi/2, and the coefficient of statis friction with the ground is very large. What is an expression for the critical angle (in radians, between 0 and pi/2) at which the yo-yo will remain motionless.

A student's car stalls right in front of a speed bump while she is on her way to physics class. To pull it over the bump, she ties a cable to her bumper and to a nearby tree, and pulls with a force, F, of 81.0 lbs (360 N) at the midpoint in a perpendicular direction.If θ is 11.0°, what is the size of the force pulling the car in lbs

Two blocks are connected by a (massless) string that runs over a (massless, frictionless) pulley as shown. Assume there is no friction between block 1 and the surface of the incline. 40° 2 If m₁ = 3.9 kg and m₂ = 5.9 kg, what is the tension in the string? Express your answer in N, to at least one digit after the decimal point.

Three coplanar forces pull from a certain mechanism. The forces have the following magnitude and direction: 80N, 0° horizontally to the right 110N, 60° from the 80N force 60N, 225° from the 80N force. Find graphically the magnitude and direction of the resultant.

Problem 4: Vector Addition. Vector A = 200 NZ45° counterclockwise from the z axis, and vector B = 300 N 270° counterclockwise from the y axis. Find the resultant R= A + B by addition of scalar components. Problem 5: Consider the picture below. Find the tension T, tension Ta tension T₂

Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If F₁ = 490 N and F2 = 400 N, determine the vector expression for the resultant R of the two forces. Then determine the magnitude R of the resultant and the angle which it makes with the positive x-axis (measured counterclockwise from the x-axis). I F2 69⁰ -1 F₁ Answers: R= j) N R = e= i B i+ i N

Two individuals are attempting to relocate a sofa by applying forces in the indicated directions. If F₁ - 650 N and F2 - 320 N, determine the vector expression for the resultant R of the two forces. Then determine the magnitude R of the resultant and the angle which it makes with the positive x-axis (measured counterclockwise from the x-axis). 50⁰ Answers: R= IN R= i i N B

A body tied to a rope moves in the plane (yxO), so that its coordinates are given by the following equations: (x(t) = Rcoswt ly(t) = Rsinwt Where R and w are positive constant Find : a) show that the velocity vector are orthongonal to to position vector. b) show that the acceleration vector always parallel to the position vector and on opposite direction and his value is v^2/R

A bicep muscle shown in Fig. P2.3 can apply a force F measured in Newtons (N) as a function of the elbow angle ϕ, measured in degrees as described by the quadratic equation F(ϕ) = 6ϕ − 0.04ϕ2. For a bicep force of F = 200 N, solve the equation for ϕ by each of the following methods: factoring, completing the square, and the quadratic formula. Using your solution from part (a), determine the elbow angle ϕ where the force exerted by the bicep is maximum. In addition, calculate the maximum force Fmax. Plot F versus ϕ and clearly indicate the maximum force on the graph. Also clearly label the x-intercepts on the graph.

Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in the figure below. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) F₂ = 205 N F₁ = 205 N 26° 26° Find the magnitude (in N) and direction (in degrees counterclockwise from the dotted line) of the total force on the Achilles tendon. XN magnitude direction X counterclockwise from the dotted line 410 25.45 What type of movement could be caused by this force? O This force can raise the heel of the foot. This force can twist the ankle to the left or right. This force can turn the foot to the left or right. This force can lower the heel of the foot.                     Needs Complete typed solution with 100 % accuracy.