Concept explainers
The normal reaction at point
Answer to Problem 13.71P
The minimum normal reaction is
Explanation of Solution
Given:
Radius of arc
Radius of arc
Mass of car and occupants is
Velocity at point
Angle of Arc from
Concept used:
Write the expression for the displacement of car from
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for the potential energy at point
Here,
Write the expression for the potential energy at point
Here,
Write the expression for conservation of energy for point
Substitute
Simplify the above expression.
Substitute
Solve the above expression for
Write the expression for the normal acceleration of car.
Here,
Apply Newton’s Law of motion for carat position
Here,
Write the expression for kinetic energy at point
Here,
Write the expression for the work done at point
Here,
Write the expression for the work energy principle for point
Substitute
Substitute
Rearrange the above expression for
Write the expression for the normal acceleration at point
Here,
Apply Newton’s Law of motion for carat position
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Simplify above expression for
Substitute
Substitute
Substitute
Simplify above for
The minimum normal reaction is
Conclusion:
Thus, the minimum normal reaction is
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Chapter 13 Solutions
Vector Mechanics for Engineers: Dynamics
- A cart has a mass of 1.5 kg. It is given some initial push toward a sensor and is slowed by a hanging mass which makes the cart turn around and speed up as it returns to its original position. This situation is illustrated in the attached image. If the acceleration towards the sensor is 0.5 m/s2 and the accaleration away from the sensor is 0.15 m/s2, a. draw the free body diagrams for the cart moving towards the sensor and away from the sensor. b. Write Newton's law for both situations and solve for the frictional force and for the force from the hanging mass.arrow_forwardThe disk D, which has weight W = 15 lb, starts from rest on an incline when the constant moment M is applied to it. The disk is attached at its center to a wall by a spring of constant k = 7 ft/lb. The spring is unstretched when the disk is at its starting position. The disk rolls down the incline without slipping. Take R = 5 ft, 0 = 25° and g = 32.2 ft/s². Use for the moment of inertia of the disk about G, IG: Figure D Part B R M mR² wwww 1 of 1 Part A - Draw a free body diagram of the disk. Indicate which forces and/or couples do work on the disk. Determine the value of the moment M for the disk to stop after rolling down a distance d = 5 ft down the incline. You must use the work-energy theorem to solve this question.arrow_forwardBeginning from rest when 0= 10°, the collar slides without friction down the fixed bar. Detemmine the speed and the rate at which the speed is changing of the slider, and the normal force exerted on bar (a) when 0= 20° and (b) when 0= 90°. R- 30 m m=30 kg Vertical planearrow_forward
- The 5.27 kg collar B rests on the frictionless arm AA! The collar is held in place by the rope attached to drum D and rotates about O in a horizontal plane. The linear velocity of the collar B is increasing according to v = 0.2 t2 where v is in m/s and tis in seconds. Find the tension in the rope and the force of the bar on .the collar if 5 s,r= 0.558 m and 0 = 58° A A' Darrow_forwardThe three masses in the figure are different. The planes do not have friction with the masses and the plane of mass 3 corresponds to a quarter of a circumference. All three masses are released at the same time. The masses m2 and m3 travel the same distance. The first mass that will reach the bottom of the ramp will be: m1 m2 m3 m2 and m3 m1 and m2 m1 and m3 they will all arrive at the same timearrow_forward3. Jet engines on the 100 Mg VTOL aircraft exert a constant vertical force of 981 kN as it hovers. Determine the net impulse on the aircraft over t = 10 s. a. -981 kN-s b. 0 kN's c. 981 kN's d. 9810 kN-s ↑ F = 981 KNarrow_forward
- The rod of the fixed hydraulic cylinder is moving to the left with a speed of 94 mm/s and this speed is momentarily increasing at a rate of 440 mm/s each second at the instant when SA = 355 mm. Determine the tension in the cord at that instant. The mass of slider Bis 0.77 kg, the length of the cord is 950 mm, and the effects of the radius and friction of the small pulley at A are negligible. Find results for cases (a) negligible friction at slider B and (b) p = 0.42 at slider B. The action is in a vertical plane. 220 mm Answers: 0.77 kg B (a) Negligible friction: T= i (b) Uk=0.42: T= i N Narrow_forwardBall B (v) with a mass of 2.0 kg is rotating in an orbit of r = 0.8 m with a velocity = = 2.4 m / s. From this moment on, find the velocity of ball B at the moment when r is 0.5 m since the rope attached to it is pulled as shown in the figure with v, = 1.2m / s. Also calculate the work required to pull the rope.arrow_forwardThe 5.2-lb cylinder is falling from A with a speed 10 ft/s onto the platform. The spring has an unstretched length of 1.75 ft and is originally kept in compression by the 1-ft long cables attached to the platform. Neglect the mass of the platform and spring and any energy lost during the collision (Figure 1) Figure FA-10 ft/s + 16 |^ 3ft -A-400 lb/fr 1 of 1 > ▼ Part A Determine the maximum displacement of the platform, caused by the collision. Express your answer to three significant figures and include the appropriate units. OF 8= 0.0914 HÅ ft Submit Previous Answers Request Answer Provide Feedback ? X Incorrect; Try Again; 5 attempts remainingarrow_forward
- Packages having a mass of 4-kg are delivered from a conveyor to a ramp with a velocity of v = 0.8 m/s. What is the velocity in which the packages will leave the ramp (at point B)? Consider e =30° andh = 12 m. The coefficient of the kinetic friction between the package and the ramp is = 0.35 Note. Please write your final answer in m/s in the provided box. Report your answer in 2 decimal places. For example: 2.34 m/s 0.8 m/sarrow_forwardPart A The 12-lb box slides on the surface for which u = 0.3. The box has a velocity v = 15 ft /s when it is 2 ft from the plate. (Figure 1) If the box strikes the smooth plate, which has a weight of 19 lb and is held in position by an unstretched spring of stiffness k = 330 lb / ft, determine the maximum compression imparted to the spring. Take e = 0.8 between the box and the plate. Assume that the plate slides smoothly. Express your answer using three significant figures and include the appropriate units. HA ? Value Units Submit Request Answer Figure < 1 of 1 < Return to Assignment Provide Feedback v = 15 ft/s 2 ftarrow_forwardThere is a 3,2kg slider ring is going down from the rest position A and slides in frictionless guide pipe as seen in the picture below. (h= 7 m). For this situation, please determine the velocity as the slider ring at B and calculate the maximum compression of the spring in millimeters. 1.2 kg h=7m. E 30° k = 24 kN/m 30° 1.5 m C Barrow_forward
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