Name PSU Email ID Section THE PENNSYLVANIA STATE UNIVERSITY Department of Engineering Science and Mechanics Engineering Mechanics 212 212H Exam 1 Tuesday February 10 2026 Problem 1 Problem 2 Problem 3 Problem 4 Total General Instructions Please read them The exam goes from 8 00 9 30 p m it is 90 minutes long You may remove the equation sheet from the front of the exam but leave the rest of the exam stapled together If you need extra space write on the back of the page Calculators are permitted during the exam You may not use a smart phone as a calculator De ne all component systems used and use proper vector notation both of these are worth points Use sin 30 D cos 60 D 1 2 and sin 60 D cos 30 D p3 2 in all your calculations Be neat and show all of your work Determining your section Section 1 Prof Zhang TR 10 35 11 50 a m Section 2 Prof Rivi re MWF 12 20 1 10 p m Section 3 Prof Gray MWF 1 25 2 15 p m Section 4 Prof Cusumano TR 3 05 4 20 p m Section 5 Prof Kube MWF 3 35 4 25 p m Section H Prof Gray MWF 11 15 a m 12 05 p m Good luck Problem 1 25 pts The slotted arm is moving to the right along the horizon tal guide at its bottom end with speed va and acceleration slotted arm is constrained to move in the cubicly shaped a when it is at A and x D 1 p3 The pin P in the p3v2 slot with equation y D x3 p3 When the pin is at A and x D 1 p3 determine the a velocity of P as a function of va b acceleration of P as a function of va c angle in degrees the velocity vector makes with re spect to the x axis d time rate of change of the speed as a function of va e radius of curvature of the path Express all vectors in the given Cartesian frame Problem 2 25 pts The incomparable Paige Bueckers is raising money for her favorite charity in a shooting exhibition In doing so she jumps above the incline and shoots the basketball perpen dicular to the incline with speed v0 with the goal of putting the ball in the hoop at B The launch point at A is in the position shown relative to the incline and the basket at B Given R and the slope of the incline as shown determine a the required launch speed v0 as a function of g and R so that the shot is successful and the ball goes through the hoop at B b the maximum height perpendicular to the incline dmax achieved by the ball during its ight to the basket Extra Credit 7 pts Determine the radius of curvature of the trajectory when the ball is on the part of the trajectory found in part b Problem 3 25 pts The hydraulic cylinder moves the pin A a constant speed v0 in a straight line along the axis of the cylinder The motion of the cylinder causes the slotted arm to rotate about the pin at O Determine r Pr P Rr and R as functions of v0 and R at the instant when D 30 Problem 4 25 pts A ball is released from rest at the surface of a container of oil The downward acceleration of the ball is given by a D g pgv where g is the acceleration due to gravity and v is the downward velocity of the ball Determine each of the following a the terminal velocity vt of the ball as a function of g b the time it takes for the ball to achieve 50 of terminal velocity as a function of g c the distance d the object has dropped when it achieves 50 of terminal velocity Hint You may nd the following integral to be helpful d D 2 ln C C where C is a constant