Given two vector functions determine the derivative of
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A box of mass 10 kg is being pulled on the floor by a mass-less rope with a force of 100 N at an angle of 60 to the horizontal. What is the acceleration of the box if the coefficient of kinetic friction between the floor and the box is
b) A ball having a mass of 0.5 kg is moving towards the east with a speed of velocity 6.0 ms-1. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 5.0 ms-1. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.
c) A block of mass 5.0 kg starts from rest and slides down a surface which corresponds to a quarter of a circle of 3.0 m radius. (i) If the curved surface is smooth, find the speed at the bottom. (ii) If the speed at the bottom is 2.0 ms-1, calculate the energy dissipated due to friction in the descent. (iii) After the block reaches the horizontal with a speed of 2.0 ms-1it slides to a stop in a distance of 1.5 m. calculate the frictional force acting on the horizontal surface. Take g=10 ms-2 .
d) A small satellite is in a circular orbit around a planet at a distance of 4.0 10 m 8 from the centre of the planet. The orbital speed of the satellite is 200 ms . 1 What is the mass of the planet
Determine the torque about the point (0, 1, 1) due to a force being exerted at the point (4, 2, 3).
बृहस्पति की दीर्घवृत्तीय कक्षा के लिए e= 0.05 है और अर्ध-दीर्घ अक्ष 7.8×10-¹¹m है। ग्रह की ऊर्जा तथा रविनीच और रविउच्च बिंदुओं की दूरियां ज्ञात करें।
A box of mass 10 kg is being pulled on the floor by a mass-less rope with a force of 100 N at an angle of 60o to the horizontal. What is the acceleration of the box if the coefficient of kinetic friction between the floor and the box is µε -0.257 Take g-10 ms.-2
किसी अवमंदित आवर्त दोलक का गति समीकरण निम्नलिखित है :
जहां m = 0.25kg, y = 0.05kgs-1 तथा k = 70Nm-1 है। (i) दोलन काल, (ii) दोलनों
की संख्या जिसके बाद आयाम का मान उसके आरंभिक मान का आधा रह जाता है, (iii) दोलनों की संख्या जिसके बाद दोलक की यांत्रिक ऊर्जा का मान उसके आरंभिक मान का आधा रह जाता है, परिकलित करें।
के लिए।