if co-efficient of friction between tyre and road is 0.5, what is smallest radious at which car turn on a horizontal road when its speed is 30 km/hr?
2.Q calculate angular speed of how hand of a clock?
3.Q A what angle must cut rack with a bend of 250m banked for safe running of trains at speed of 72km/hr?
4.a force of 5kgwt acting on a body changes its vilocity from 20 cm/s to 1000 cm/s in 20s. calculate the mass of body, g=9.8 m/s2 ?
One post per problem, please, it gets much to cofusing.
Now, what have you done on these? What is your thinking>
1. To determine the smallest radius at which a car can turn on a horizontal road, we can use the concept of centripetal force. The formula for centripetal force is F = m * v^2 / r, where F is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the turn.
First, we need to convert the speed from kilometers per hour (km/hr) to meters per second (m/s). Since 1 km/hr = 1000 m/3600 s, the speed of the car is 30 km/hr * (1000 m/3600 s) = 8.33 m/s.
Now, let's substitute the values into the formula. Since we're looking for the smallest radius, we assume the car is at the verge of slipping, which means the maximum frictional force is acting. The maximum frictional force is given by F_friction = coefficient of friction * normal force.
Since the car is on a horizontal road, the normal force is equal to the weight of the car, which is m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, F_friction = coefficient of friction * m * g.
Setting F_friction equal to the centripetal force, we have coefficient of friction * m * g = m * v^2 / r. Simplifying the equation, we get r = v^2 / (coefficient of friction * g).
Substituting the known values, we find r = (8.33 m/s)^2 / (0.5 * 9.8 m/s^2) ≈ 7.2 meters. Therefore, the smallest radius at which the car can turn on a horizontal road at a speed of 30 km/hr is approximately 7.2 meters.
2. The angular speed of the hour hand of a clock can be calculated based on the formula 2π radians / 12 hours. Since there are 360 degrees in a circle and 12 hours on a clock, we can convert the angular speed to degrees per hour.
Using the unitary method, we have 2π radians = 360 degrees, so the angular speed is 360 degrees / 12 hours = 30 degrees per hour. Therefore, the angular speed of the hour hand of a clock is 30 degrees per hour.
3. To determine the angle at which a rack with a bend of 250 meters should be cut for safe running of trains at a speed of 72 km/hr, we can use the banking angle formula. The formula is given by tan(beta) = v^2 / (g * r), where beta is the banking angle, v is the velocity, g is the acceleration due to gravity, and r is the radius of the turn.
First, convert the speed from kilometers per hour (km/hr) to meters per second (m/s). The speed of the trains is 72 km/hr * (1000 m/3600 s) = 20 m/s.
Substituting the values into the formula, we have tan(beta) = (20 m/s)^2 / (9.8 m/s^2 * 250 m). Simplifying the equation, we find tan(beta) ≈ 1.65.
To find the angle beta, we take the inverse tangent (arctan) of both sides of the equation. So beta ≈ arctan(1.65).
Using a calculator or trigonometric tables, we find beta ≈ 58.11 degrees. Therefore, the rack should be cut at an angle of approximately 58.11 degrees for safe running of trains at a speed of 72 km/hr.
4. To calculate the mass of a body based on the given information, we can use Newton's second law of motion, which states that force equals mass times acceleration (F = m * a). In this case, the force is the change in momentum of the body over time.
First, we need to calculate the change in velocity (delta v) using the given values. The change in velocity is 1000 cm/s - 20 cm/s = 980 cm/s.
Now, we convert the change in velocity to meters per second (m/s) by dividing by 100: 980 cm/s / 100 = 9.8 m/s.
Next, we calculate the average acceleration (a) using the formula a = delta v / t, where t is the time. From the given information, the time is 20 seconds. Therefore, a = 9.8 m/s / 20 s = 0.49 m/s^2.
Using Newton's second law, F = m * a, we rearrange the equation to solve for mass (m): m = F / a.
Since the weight of the body is given as 5 kgwt (kilogram weight), we need to convert it to a force by multiplying by the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the weight in newtons is 5 kgwt * 9.8 m/s^2 = 49 N.
Now we substitute the values into the formula to find the mass: m = 49 N / 0.49 m/s^2 = 100 kg.
Therefore, the mass of the body is 100 kilograms.